We were introduced to the concept of Trigonometry this week. We also learned about three buttons on the calculator. sin, cos, and tan. These words are actually shortened, and they mean “sine, cosine, and tangent”. Trigonometry will usually involve right triangles, but isosceles and scalene triangle are able to be solved through trigonometry. Trig questions usually ask for the length of one side of a triangle, while giving you a reference angle, along with the length of a single side.
How do we solve these? First, each side has a specific name, depending on where the reference angle is. The names are adjacent, opposite, and hypotenuse. The hypotenuse will always be the line opposite from the right angle. The adjacent line is the line closest to the reference angle that is not the hypotenuse. The opposite line is the line farthest from the reference angle that is not the hypotenuse. Got it? Good.
You’ll have to learn the phrase SOH CAH TOA. The beginning of each word represents some specific buttons on the calculator, namely sin, cos, and tan. The last two letters of each word represent the lines of a triangle. You remember “Adjacent, Opposite, and Hypotenuse”, correct? If you have to solve for the length of the opposite line, and are given the length of the hypotenuse along with a reference angle, the question is a sine question. Sine(reference angle)=
The best way to figure out what sort of trig question lays in front of you is to remember the phrase SOH CAH TOA.
Now take a look at some of these questions below. All problems require you to solve for x. The first one is a sine question. How do we know? The opposite line is represented by x, while the hypotenuse is represented by 7. The reference angle is 27. The equation is sin27=
7 multiplied by sin27 (approx. 0.454) is 3.2.
The opposite line is 3.2 units long.